This week BA stopped their pet service to UK. Mainly due to the huge backlog of 1000s of requests per day for the 8 spots available. Due to new passenger ban, BA are unable to ship.
Cathay are still undecided if they will continue or not but have raised their rates substantially across the board. Dont expect much change out of 50k for shipping a cat.
Excess baggage to Amsterdam then pet taxi to UK is now the most realistic way to get your pet to UK but expect this to get difficult as 1000s of pet holders are waiting to move. Dont think this will ease up till the BNO migration slows down.